🔗 BEAM Chain Networking Simulator 🧩 Problem Overview We aim to gossip and aggregate num_signatures post-quantum signatures (each of size signature_size) across the network within a time limit max_time_seconds. Each signature is initially owned by one of num_validators validators.Among these validators, a subset can act as aggregators (num_aggregators) or global aggregators (num_global_aggregators), capable of performing aggregation at a rate of aggregation_rate_per_sec (signatures per second). The result of each aggregation is a recursive SNARK proof. This allows: Combining multiple individual signatures into a single aggregated SNARK. Further aggregating those SNARKs into higher-level proofs recursively.

Pairings and applications slide: https://hackmd.io/@jVkDzwsSRbCqx36bM2T_dA/rk_XGdnVT Prime finite field A prime field consists of numbers $0,1,2,...,p-1$ where $p$ is prime Math operations are defined as follows: $a+b: (a+b)\pmod{p}$ $a\cdot b: (a\cdot b)\pmod{p}$ $a-b:(a-b)\pmod{p}$

Polkadot Host implementations use Fast/Warp sync to synchronize missing block headers. They are followed by the state sync. The faster we can synchronize missing block headers and the most recent state, the faster our node will be able to start executing the most recent blocks and create new blocks (if we are running validator). In this post we will explore current strategies to sync the state as well as propose a new approach. The goal is to come up with state sync protocol that: 1. Easily parallelizable 2. To save bandwidth responses do not contain overlapping data 3. Resistant to DOS attacks If you are already familiar with how state sync works, just scroll down to Proposed solution section. State